Bayram Tutumlu has been involved in deals to take a number of players to the Liberty Stadium since Laudrup succeeded Brendan Rodgers in the summer of 2012.
He has been informed that his services are no longer required, with Swans chairman Huw Jenkins looking to take transfer policy in a different direction.
Laudrup's future in South Wales had already been called into question prior to Tutumlu's exit, with Paris St Germain among those said to be keen on bringing the Dane into their dugout.
He is, however, adamant that he has no plans to quit his post and intends to guide the 2013 League Cup winners into a new campaign.
Laudrup said: "It is their (Jenkins' and Tutumlu's) mutual problem. It does not affect my relationship with Bayram. And it does not alter my decision to stay at Swansea.
"The only thing I'm interested in his having the best players available in the next season."
Tutumlu's has backed up that stance, insisting Laudrup has no intention of moving elsewhere.
He said: "Michael Laudrup is the coach of Swansea City and he will stay as the coach. He thinks only about Swansea. He has said many times before that he will stay at Swansea.
"I've not spoken to Michael, but I'm very disappointed about the situation.
"I only try to bring good players for Michael while Huw Jenkins wants cheap, Championship players. I did a lot of good work for Swansea and I helped to bring players like Chico Flores, Michu, Pablo Hernandez and Jonathan de Guzman to the club."